New Transfer Students in places where school uniforms are a cultural default setting often wear their old ones until the school can provide them with a new one. In fiction, this shows the newcomer or outsider. When they get the current school uniform, this indicates they've been assimilated. If the student is meant to be a Fish out of Water, they will keep their old uniform throughout the series. In Japanese media, even rebels don't choose to abandon uniforms entirely; in American media they will do this even if the new school doesn't have uniforms. Compare the Non-Uniform Uniform.

Aside from the "assimilation" thing, it's worth mentioning that school uniforms normally aren't just stored in bulk somewhere in the school's designated warehouse of uniforms. That'd be ridiculous because all students have different measurements. Can you imagine the amount of unused uniforms of all shapes and sizes?

Each student orders their uniform before the year begins, and they all get it on time. Students that transfer in the middle of the year have to order their uniform separately from all other students, and may even have to wait until the required materials are shipped to the factory. So there's really nothing unusual going on, just everyday life stuff.